1. Field of the Invention
The present invention relates to the measurement (for example the calibration) of angular displacement of a rotary table. For a proper understanding of the present invention and its advantages, it is first necessary to consider the prior art.
2. Description of the Related Art
FIG. 1 illustrates a prior art calibration apparatus. The apparatus comprises an object table 10 having a stator 12 and rotor 14. The rotor 14 has a positioning system 16 for positioning the rotor 14 relative a datum D1 provided on the stator 12. The positioning system 16 typically comprises e.g. a position servo 17 which responds to demand data from a user to position the rotor 14 relative to stator 12, together with an encoder (not shown) whose output is displayed on a digital read-out DRO. Mounted to the object table 10 is an intermediate table 20 having a stator 22, fixedly mounted to the rotor 14 of the object table 10, and a rotor 24 having a scale 26 for determining angular displacement of the rotor 24 relative to the datum D1. The scale 26 provided on the rotor 24 of the intermediate table 20 is an exceedingly accurate scale; typically accurate to within 0.1"arc second. The object of a calibration operation is to calibrate the positioning system 16 of the object table 10.
To this end the rotor 24 supports a housing 30 for a pair of retro-reflectors RF1 and RF2 which form part of an angular interferometer measurement system (also shown in FIG. 2). The angular interferometer comprises a laser beam L1 emitted from a laser 32 which is split by a beam splitter 34 into two parallel beams L2 and L3. The beams L2 and L3 are incident respectively upon retro-reflectors RF1 and RF2, and consequently returned upon their incident path to interfere with each other at a detector (not shown). Rotation of the retro-reflector housing 30 about axis A, (as a result of rotation of the rotor 24) causes a shift in the interference fringes in the interfering beam at the detector. If the interferometer has been datumed with the retro-reflectors RF1 and RF2 lying in a plane exactly perpendicular to the incoming beams L2 and L3, then the following equation holds true: EQU R=K Sin .THETA. (1)
where:
.THETA. is the angular displacement
R is the number (not necessarily a whole number) of interference fringes; and
K is known as the scale factor and: EQU K=2Dn/.lambda.o (2)
where
D is the distance between the retro-reflectors RF1 and RF2
n is the refractive index of air
.lambda..sub.o is the wavelenth of the laser light in a vacuum.
Calibration of the positioning system 16 of the object table 10 is achieved by first of all datuming the interferometer so that the retro-reflectors RF1 and RF2 are as close as possible to a position perpendicular to the beams L2 and L3. Thereafter, for all operations and calculations, exact orthogonality of beams L2 and L3, and retro-reflectors RF1 and RF2 is assumed. The positioning system 16 is then used to rotate the rotor 14 to a given angular displacement (e.g. 120.degree.) as measured by the positioning system, and counter-rotating the rotor 24 of the intermediate table by the same amount (as measured by the scale 26 of the intermediate table). Any net angular displacement from the datum between the two rotations (as a result of an inaccurate rotation of rotor 14 by the positioning sytem 16) is measured using the interferometer. Thus, the following relationship holds true: EQU .THETA..sub.object table =.THETA..sub.intermediate table +.THETA..sub.Interferometer ( 3)
where:
.THETA..sub.interferometer is the angle calculated from differential linear displacement of the retro-reflectors RF1 and RF2 from the datum position mentioned above (when the plane in which the retro-reflectors RF1 and RF2 lie is perpendicular to the incident beams L2 and L3).
Subsequent calibrations of other angular displacements (for example 121.degree.) are performed by once again rotating the rotor 14 from the datum position to the displacement to be calibrated.
In practice, the rotor 24 of the intermediate table 20 is effectively "counter-rotated" by constraining the rotor 24 from moving during rotation of the rotor 14. This method of "counter-rotating" has a number of advantages:
a) Firstly, it ensures that the laser beam incident upon, and reflected from the retroreflectors remains unbroken.
b) Secondly, it obviates the need to provide a positioning system for the intermediate table.
c) Finally, it reduces the errors in the calibration.
This is because the error on .THETA..sub.interferometer, .DELTA..THETA. is given by the following expression: EQU .DELTA..THETA.=(R.sup.2 .DELTA.K.sup.2 +K.sup.2 .DELTA.R.sup.2)1/2(4)
inevitably, because the operation is carried out over a number of hours, the value of the scale factor K will vary over the time required to perform the calibration; typically, as a result in a variation of the temperature of the air (thus altering the refractive index of air). In the above equation, the term giving the variation in K (.DELTA.K) is multiplied by R, and since R increased with increasing .THETA. the error in the measurement of angular displacement (.DELTA..THETA.) is directly proportional to the magnitude of angular displacement. Thus, for example, measurement of an angular displacement of 1.degree. will have half the error due to the variation in K, compared with a measurement of an angular displacement of 2.degree.. It is thus typically necessary in the prior art method, in order to achieve the desired accuracy, to constrain the rotation of the retro-reflector housing 30 (i.e. .THETA..sub.interferometer) to a maximum of approximately 1.degree..
Thus, the prior art method has the disadvantages of requiring an extremely accurate, highly expensive intermediate table 20, and the requirement of restricting the rotation of the rotor 24. These disadvantages are in addition to the disadvantage associated with the stringent datuming requirements for the interferometer which inspite of being time continuing introduces error into the data.